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lbvjy [14]
3 years ago
10

A closed rectangular box with a sqaure

Mathematics
1 answer:
deff fn [24]3 years ago
6 0

Answer:

  4 inches on each edge of the cube

Step-by-step explanation:

A closed box will have minimum area when it is a cube. For a volume of 64 in^3, the edge length must be ∛64 = 4 inches.

_____

Using derivatives, the base edge length can be defined as x, and the surface area as ...

  S = 2x^2 + 4x(64/x^2)

This is minimized when dS/dx = 0:

  dS/dx =- 4x -256/x^2 = 0

  x^3 = 64

  x = ∛64 = 4 . . . . . should look familiar

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What is the solution to this inequality?<br> –16x &gt; –80
Kisachek [45]

Answer:

x < 5

Step-by-step explanation:

–16x > –80

Divide each side by -16, remembering to flip the inequality

-16x/-16< -80/-16

x < 5

7 0
3 years ago
A lab assistant needs to create a 600 mL mixture that is 3% hydrochloric acid. The
OlgaM077 [116]

Answer:

240 ml of 1.5% solution and 360 ml of 4% solution should be used.

Step-by-step explanation:

Since a lab assistant needs to create a 600 mL mixture that is 3% hydrochloric acid, and the assistant has solutions of 1.5% and 4% in supply at the lab, to determine the number of milliliters of the 1.5% solution and the number of milliliters of the 4% solution that must be used, the following calculations must be performed:

50 x 0.015 + 50 x 0.04 = 0.75 + 2 = 2.75

40 x 0.015 + 60 x 0.04 = 0.6 + 2.4 = 3

600 x 0.4 = 240

Therefore, 240 ml of 1.5% solution and 360 ml of 4% solution should be used.

4 0
3 years ago
Can u guys help me with y?
Anton [14]

Answer:

Step-by-step explanation:

Given condition

y = x + 5

When x = - 1

y = - 1 + 5 = 4

when x = 0

y = 0 + 5 = 5

when x = 1

y = 1 + 5 =6

hope it helps :)

3 0
3 years ago
Ivan chases a goat for 41 seconds. He runs at 7 meters per second.<br> How far does he go?
andre [41]
If he runs 7 meters per second for 41 seconds, then his total distance is 41 x 7, which is 287 meters
4 0
3 years ago
Read 2 more answers
The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method
inessss [21]

The bounded region we're concerned with lies above the x-axis.

y^2-x^2=1\implies y=\sqrt{1+x^2}

This hyperbola intersects with the line y=2 for

2=\sqrt{1+x^2}\implies4=1+x^2\implies x^2=3\implies x=\pm\sqrt3

Using the washer method, the volume of the resulting solid is

\displaystyle\pi\int_{-\sqrt3}^3(2^2-(\sqrt{1+x^2})^2)\,\mathrm dx=2\pi\int_0^{\sqrt3}(3-x^2)\,\mathrm dx=\boxed{4\pi\sqrt3}

5 0
3 years ago
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